△ABC is similar to △PQR. Length of AB is 18cm and length of the corresponding side PQ is 12cm. If area of △ABC is 324sq cm, what is the area of △PQR?
- A72sq cm
- B144sq cm
- C36sq cm
- D487.5sq cm
Solution & Step-by-step Explanation
For similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides:
Area(△PQR)
Area(△ABC)
=(
PQ
AB
)
2
Area(△PQR)
324
=(
12
18
)
2
Area(△PQR)
324
=(
2
3
)
2
=
4
9
Area(△PQR)=
9
324×4
=36×4=144sq cm
Area(△PQR)
Area(△ABC)
=(
PQ
AB
)
2
Area(△PQR)
324
=(
12
18
)
2
Area(△PQR)
324
=(
2
3
)
2
=
4
9
Area(△PQR)=
9
324×4
=36×4=144sq cm